The Stacks project

Lemma 62.8.4. Let $f : X \to S$ be a morphism of schemes. Assume $S$ locally Noetherian and $f$ locally of finite type. Let $r \geq 0$ be an integer. Let $\alpha $ be a relative $r$-cycle on $X/S$. Let $g : S' \to S$ be a surjective morphism. Then $\alpha $ is effective if and only if the base change $g^*\alpha $ is effective.

Proof. Omitted. $\square$

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